Localization transition in symmetric random matrices

We study the behavior of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully connected Lévy matrices. We derive a cr...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2010-09, Vol.82 (3 Pt 1), p.031135-031135, Article 031135
Main Authors: Metz, F L, Neri, I, Bollé, D
Format: Article
Language:English
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Summary:We study the behavior of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown.
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.82.031135